Skipper Rhys Ruddock crossed for a brace of tries to prevent a shock loss for Leinster in Parma in their opening URC game.
Leo Cullen’s men looked set for another landslide win over the Italians when they eased their way into a 21-0 lead after just 26 minutes.
But in the end it took a scrambling defence all they had to prevent a shock first loss to Zebre in 17 games.
In the end Leinster’s win was as much down to sloppy handling from the Italians preventing them from securing a winning try from a handful of promising chances in the dying moments, while three missed conversions also proved costly for a Zebre side who brought in 21 players during the summer.
Leinster looked well on their way to victory when they turned around leading by 28-10 in the Italian sunshine, but once Zebre got their act together it was a different story.
Zebre, who only secured one victory last season, won the second-half 19-5 and that will be a source of worry to the former champions who are still trying to get last season’s home semi-final loss to the Bulls out of their system.
Leinster made the most of early Zebre indiscipline with scrum-half Luke McGrath darting over for his 42nd try after five minutes.
Skipper Ruddock then struck for a brace of tries in six minutes as they turned the screw.
The 31-year old got over at the end of the opening quarter after summer signing from Munster Jason Jenkins had delivered a lineout off the top.
Referee Ben Blain finally lost patience and Zebre skipper David Sisi was binned when he conceded their seventh penalty, but while Ruddock got over after they went to touch down the right, the Italians enjoyed their best spell when down to 14 men.
A knock-on by Ross Molony after a restart gave Zebre a platform and they worked it wide for South African Richard Kriel to get over for an excellent try on the half hour.
That got the small Italian crowd on their feet and they had more to cheer three minutes later when a crosskick from Eden was taken by Bruno and he chipped over Max O’Reilly to score in the right corner.
However, Leinster finished the half strongly when Jenkins crowned a good debut when he got over with the help of Max Deegan and Ed Byrne after another lineout off a penalty.
Zebre got on top after the restart and looked danergous when the ball went wide, and they got a great boost after 50 minutes when Simone Gesi scored in the left corner when he escaped Rob Russell’s tackle after another swift move across the line.
South African MJ Pelser then burst through Jamie Osborne’s weak tackle to score under the posts, with Tiff Eden’s first conversion of the afternoon cutting the gap to 28-22 after 56 minutes.
Dave Kearney eased the concerns of the visitors after 61 minutes when a good pass from Ciaran Frawley, on for full-back Max O’Reilly, sent the winger over for his 53rd Leinster try, with Ross Byrne missing his first conversion of the afternoon from the left.
Frawley and Kearney were guilty of poor defending nine minutes later when Franco Smith Jnr, son of the new Glasgow and former Italian coach, squeezed through them, with Eden’s conversion cutting the gap to four and set up a very nervous finish but in the end Leinster just about held on.
Scorers: Zebre Parma: Tries: R Kriel, P Bruno, S Gesi, MJ Pelser, F Smith. Cons : T Eden (2).
Leinster: Tries: R Ruddock (2), L McGrath, J Jenkins, D Kearney. Cons: R Byrne (4).
Zebre Parma: R Kriel (J Trulla 64); P Bruno, E Cronjé (F Smith 63), E Lucchin, S Gesi; T Eden, C Cook (A Fusco 63); P Buonfiglio (J Pitinari 54), J Du Toit (L Bigi 46), M Nocera (M Hasa 46); D Sisi, L Krumov (J Furno 64); L Andreani (G Volpi 64), MJ Pelser, T Fox-Matamua.
Leinster: M O'Reilly (C Frawley 53); R Russell, J Osborne, C Ngatai, D Kearney; R Byrne, L McGrath (N McCarthy 63); E Byrne (M Milne 53), R Kelleher (J McKee 64), M Ala'alatoa (V Abdaladze 72); R Molony, J Jenkins (B Deeny 53); R Ruddock (A Soroka 6, 76), S Penny (W Connors 53), M Deegan.
Referee: Ben Blain (Scotland).
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